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How bad would nuclear winter caused by a US-Russia nuclear exchange be?

I think the issue is not the energy source/density, the issue is amount of particles in the atmosphere, Sagan/TTAPS is on record saying that the amount of particles is the same magnitude in the Kuwait fires as in their model, in addition at least in theirs simulations the burning of oil/gas deposits within cities like in gas stations cars etc... is what produced the most amount of the particles and particles in the correct mass that would rise and produce the most damage by "self lofting" into the upper layers - hence his predictions.

Also the the nuclear mushroom is completely irrelevant it contributes negligible amounts to particles in the atmosphere, it is not surprising that some smoke is thrown from the blast, but to get "Nuclear Winter" from the model/simulations the main source are the fires and the proposition that the particles will "self loft" and rise and rise and rise....., yet it seems that the fires do not produce any "self lofting", in addition as far as i recall they are also not blocking as much of sun energy as proposed.

Note that it is not that they were a little off, they were completely wrong, more over it was probably completely politically motivated (it is for a good cause so it is ok to inflate inflate and inflate) but we should be really skeptical.

How bad would nuclear winter caused by a US-Russia nuclear exchange be?

Resubmitting since it seems the comment was lost.

The whole "Nuclear Winter" field of modeling was born in sin and hence must be suspect.

As far as I kno​​w the original models and simulations and the whole concept was promoted by Carl Sagan et el. ( TTAPS team i.e.  Richard P. Turco, Owen Toon, Thomas P. Ackerman, James B. Pollack and Carl Sagan) from what seems to be almost purely political reasons and a transparent PR campaign i.e. "was with the explicit aim of promoting international arms control" - which might not be a bad political goal, but always results in bad science.(Also disappointing is that a science educator and a "science/skepticism hero" like Sagan is actually a political hack).

Luckily during the Gulf war the concept came to be empirically tested after Saddam ignited the Kuwait oil wells.

TTAPS predicted :
"stated that they expected catastrophic nuclear winter like effects with continental-sized effects of sub-freezing temperatures ... as a result of the Iraqis going through with their threats of igniting 300 to 500 pressurized oil wells that could subsequently burn for several months. "

In reality 600 wells burned for 8 months.

In the popular media Sagan argued: "that some of the effects of the smoke could be similar to the effects of a nuclear winter.... resulting in global effects. He also argued that he believed the net effects would be very similar to the explosion of the Indonesian volcano Tambora in 1815, which resulted in the year 1816 being known as the Year without Summer. "
" Sagan stressed this outcome was so likely that "It should affect the war plans. "


In reality nothing happened

Sagan later conceded in his book The Demon-Haunted World that his predictions obviously did not turn out to be correct: 
"it was pitch black at noon and temperatures dropped 4–6 °C over the Persian Gulf, but not much smoke reached stratospheric altitudes and Asia was spared."
(Yes spared..really?...Asia was not "spared" it just that the models and the threat were not real)

The atmospheric scientist tasked with studying the atmospheric effect of the Kuwaiti fires by the National Science Foundation, Peter Hobbs, stated that the fires' modest impact suggested that "some numbers [used to support the Nuclear Winter hypothesis]... were probably a little overblown."
("a little overblown"...I guess this is sarcasm)

Were the empirical data from the Gulf-War "natural experiment" incorporated into this model?
It is easy enough in a model to get any results you want, the important thing to ask is how they were tested, how is this models prediction can be applied to Gulf war data and how they predict the weather effects of 1991? or any other such events.